You can’t believe the government’s numbers on employment. Take it from the guy who used to run the government’s numbers on employment.

Keith Hall, the former head of the Bureau of Labor Statistics, which produces the federal government’s monthly jobs report, told New York Post columnist John Crudele that the official unemployment rate of 7.6 percent is wrong and might be too low by 3 percentage points, according to Crudele’s column on Thursday.

Though Hall now works for the Mercatus Center, a right-wing think tank at George Mason University partially funded by the billionaire Koch Brothers (Charles Koch sits on its board), he is not suggesting that the BLS is cooking the books, as Jack Welch and other conservatives have suggested.

What he is saying is that the unemployment rate doesn’t capture all of the people sitting on the sidelines in despair of finding a job. The employment-population ratio, the percentage of the working-age population actually working, sits at 58.7 percent, Hall notes, well below a peak of 63 percent before the recession and the lowest rate since the early 1980s. This suggests to Hall that there are a lot of people not showing up in the official unemployment rate.

I’d personally focus on the labor-force participation rate, which includes people working and looking for work. This has been at about 63 percent in recent years, well below the 66 percent that prevailed before the recession. That may not sound like a big difference, but that extra 3 percent would take the number of officially unemployed people up to about 18 million from 12 million.

And that would jack the unemployment rate up to about 11 percent. Which, yikes.

So tomato, tomahto, let’s call the job market awful. Hall also points out that the seasonal adjustments the BLS makes to the employment numbers have been skewed ever since the massive recession blew a big hole in the numbers.

None of these are particularly controversial ideas. In fact, Federal Reserve Chairman Ben Bernanke has hinted a few times in congressional testimony this week that he doesn’t fully buy the unemployment rate,calling it “in some ways … too optimistic a measure of the state of the labor market.”

Bernanke might not believe that unemployment should really be 11 percent, but he also doesn’t believe it is as low as 7.6 percent. And he has suggested that he will still be skeptical when it hits 6.5 percent, which he says is the “threshold” for the Fed to start thinking about raising interest rates from zero.

Given the ongoing suffering in the labor market, though, it is a wonder that the Fed is talking about pulling back on stimulus by slowing down its $85 billion a month in bond purchases in the near future. Half of the Fed’s job is promoting maximum employment, and the job market needs all the help it can get.